There are many variations of the exact same principle that Feynman expressed. In software engineering, one of them is Rubber Duck debugging:
How could explaining your problem to a rubber duck be anything but a waste of time? Turns out that having to articulate your problems to an audience (even a fake one) helps clarify those problems. I don’t use an actual rubber duck, but I can’t tell you how many problems I’ve solved because I started writing an email and halfway through I realized that I missed an entire avenue of investigation or false assumption I made.
Sure, some researchers can probably get by locked in a room for years at a time. I suspect this is a minority, even at the highest levels.
But they’re not “locked in a room”. They’re constantly interacting with talented hand-picked graduate students. They attend conferences. They constantly interact with peers.
The thing you’re describing with software is generally accomplished through design walk-throughs. I was skeptical of these at first, but actually found them useful; even if they didn’t uncover technical issues, experienced participants might uncover institutional issues.
I think there is a difference between a researcher and a professor. If you want to be just a researcher then go ahead and isolate yourself from lowly students and just grind away without helping the next generation.
IMHO a professor has an obligation to teach and pass along knowledge to the next generation.
That’s absolutely not how it works in academia. A professor is expected to do research and teach. But at a sufficiently advanced level of seniority and reputation, “teaching” means mentoring graduate students engaged in collaborative research, not preparing lecture slides for an undergraduate class.
Well yes, that’s one of the bigger problems in academia and education today. The culture of denigrating teaching is infectious. We get garbage research from researchers hell bent on publishing at the cost of all else.
Wait, graduate students aren’t real students? Teaching and mentoring them isn’t real teaching? Helping them with their doctoral dissertations on their own research that will launch their careers isn’t “passing along knowledge to the next generation”?
Only two researchers (Chin-Ning Yang and Eric Maskin) have won a Nobel Prize (in Physics and Economics respectively) for work that was substantially done at IAS. Contrast this with 40 for Harvard (University or Medical School), 26 for MIT, 26 for Stanford, 22 for Cal, 20 for Caltech, 20 for Cambridge, 19 for Columbia, 18 for Princeton, 12 for Oxford, 9 for Cornell, 7 for Hopkins. There are certainly many accomplished people at IAS and the model has been replicated elsewhere but in general there is little “spectacular record of accomplishment”, in no small part because they typically recruit people after their most fruitful years of early research but also because they don’t have either the impetus or incentives to pursue diverse lines of research. Albert Einstein, as an example, after a long career of collaborating with many other scientists in a diverse array of problems in emerging area of physics, spent the last twenty-odd years at IAS fruitlessly trying to develop a unified field theory, arguing against the standard interpretations of quantum mechanics (both Copenhagen and De Broglie–Bohm and most definitely opposed to any kind of ‘Many Worlds Theory’), and taking walks with Kurt Gödel, all while other researchers in the academic world continued to advance general relativity and quantum field theory.
The issue is that “just grind[ing] away” is not generally how innovation occurs. Collaboration, having to look at old problems in a new way by answering basic questions of ‘Why?’, and being surrounded by younger and ambitious talent with fresh ideas spurs on most real innovations. I suspect most academics would relish in being rid of the bureaucracy and stilted culture of modern academia but most do like explaining things to students (even if preparing lectures and grading tests is a bore to be shunted off to graduate teaching assistants) and answering the insightful questions of the occasional brilliant student and encouraging and advising them is both rewarding and inspiring to keep doing new work and unexplored ideas.
By the time someone is a graduate student, they are expected to be able to learn most things on their own (outside of actual grad-level course, which are a minority of what a PhD candidate will do). I’m sure there are some professors who will devote time to mentoring their students regularly but most are really looking for graduate researchers who can work on their own without asking basic questions or needing a lot of detailed guidance, and students are mostly responsible for working on their doctoral dissertations with pretty minimal involvement until it is close to ready to present for defense. Unless the thesis project aligns closely with and contributing to the professor’s own direct area of research they are probably only casually involved in the actual work and have little daily interaction with what their grad students are doing.
IAS claims 36 Nobel Laureates, but maybe they’re fudging the numbers by citing individuals who won the Nobel for work that was done prior to becoming IAS faculty. I’m not out to defend IAS. I will, however, defend researchers who find it more productive – both for themselves and for society as a whole – to confine themselves to research and mentoring graduate students and post-docs in collaborative research rather than preparing slides for undergraduate classes and all the other menial tasks associated with undergraduate courses, even with the help of TAs.
That may sometimes be true to some extent, but in my experience, graduate students and post-docs are closely involved in the principal investigator’s research, their dissertations are closely aligned with it (or at least, pertinent to it), and, FWIW, they’re even part of their mentor’s social life. It’s often like an academic “family”. Which is a far cry from the implication that they’re isolated self-learners working on their own.
Well, that’s certainly the dream but I suspect if you did a broad survey you’d find that the reality is not so rosy, at least in STEM fields. Often as not today a professor is spending more time developing grant proposals and securing funding (and if truly ambitious, advancing through the department ranks to a chairmanship and maybe even moving into administration if they are a true nimrod) than actually leading the research, and while they may be listed as the principal investigator and lead author on every paper they may spend little enough time in the lab doing actual research. I can’t say that I’ve ever seen or heard of a professor who materially helped their graduate students write a dissertation (nor should they beyond providing feedback), and many don’t even want to review an in-process dissertation until the graduate student thinks it is ready for defense.
As for the “academic ‘family’” and “even being part of their mentor’s social life”, I can only offer that most of what I hear from graduate students (including the program I was in for a period and another that I seriously considered applying to) was quite the opposite; the advisor-student relationship was purely transactional and graduate students are cheap, pseudo-indentured labor encouraged to produce enough work to be worthy of publication which the student would write and the professor would take prime authorship of. I had a more involved academic and familial relationship with the professor I worked for as an undergrad on the aforementioned software project than I saw anyone have in a PhD program, which helped turn me off from pursuing a doctorate. When I TA’d I was basically handed a series of lecture notes and warned to prepare to take over a lecture if the prof didn’t show (which didn’t happen to me but I had an EE class where that was a somewhat regular occurrence) and then had to run a study session and answer questions with no guidance whatsoever on a topic that I had just covered the previous semester. From what I’ve heard (and I’ve casually advised a handful of people going into PhD programs and gotten regular feedback on how it is going) that has only gotten worse in the decades since my experience, to the point of some having openly adversarial relationships with advisors but continuing on rather than losing the invested time and restarting their entire program.
I have a friend whose advisor (according to him) had students pick up her dry cleaning and other similarly crucial academic work. Big microbiology group. She was not in the lab day to day, of course; she was the big-shot principal investigator.
I recall a story about a student (Dijkstra?) who’s solved a problem as an undergrad (MA?) and their thesis advisor just told them to write it up for their PhD and it would be accepted, but prodigies still generally get undergrad degrees. What classes did Terrance Tao take as an undergrad? Mostly general education electives + grad level math and finish in 2 years?
I didn’t have a good graduate school experience. My advisor was a fucking prick and I was a shitty researcher. I was an outstanding TA though and I managed to squeak out a MS. I was accepted as what they called a terminal master’s. If I was good at research I probably could have found a professor to take me on and I would have been upgraded to a PhD student. People who were accepted as a PhD student and dropped out after putting in a couple of years were given a master’s as a booby prize and even if they did end up finishing the PhD they were awarded a master’s at some point along the journey. So she will likely get a master’s along the way and maybe a bachelor’s as well. So a Colorado school teacher may well be a possible career choice.
Speaking as a current PhD student (though in the UK, which doesn’t have quite the same culture) there’s just a huge level of variation.
A friend of mine, a fellow student, is getting married this week; her supervisor is going to be the best man. I’ve stayed at my own supervisor’s house and just gone round for dinner, she’s looked after my plants while I was on holiday, she buys me birthday presents. She used to take her previous student- and her daughter- on days out and babysit. I’ve not been given other people’s work to do at all, I’ve been turning down help. I’ve had plenty of chaos in the project, but my supervisors have frankly gone above and beyond to help.
But I also know students who have had a terrible experience, given no support and just expected to produce results for a completely absent PI. I’ve heard of others who have literally been made to compete for research; supervisors giving two of their students the same project, whoever finishes first can count it towards their thesis, while the loser has to start a new project from scratch… This in a country where PhD funding is time limited so you have 3-4 years to complete, and students have a personal project budget (though many use supervisor budget as well, with permission). I know people who have completed their PhD who just start crying if anyone mentions their supervisor, because they still can’t talk about it.
People are different, supervisors no less than others, some are lovely people, some are not. The issue here at least is that in many situations, they have all the power; if they control the funding and they want to be an appalling bully, they can be.
By the way, perhaps someone with more experience with differential equations could comment on the original paper? The techniques involved and for what they are useful, and the significance of the result? I feel like I could learn something.
Huh, I never knew I used to “rubber duck.” Way back when I was a baby programmer, my IT department had a position called POD - the Programmer of the Day. It was a rotating position among experienced programmers, and for that day, they sat in a different office – technically, a very small office. And all day they’d be available to answer questions. If no one called or dropped by, they’d just do their own work.
Anyway, I often found to best way to get around a problem that was flummoxing me was to go explain it to the POD. And very often I’d get halfway through, stop, and realized I’d found the solution myself.
I don’t think it has much to do with differential equations; it’s measure theory and/or functional analysis (neither of which are areas of expertise for me).
Back to the case at hand, I do find it somewhat implausible that she “hasn’t finished high school”. For a home-schooled student, “finishing high school” would be defined by passing a test from the state, and one of the advantages of home-schooling is that a student can work at their own pace. Now, for most home-schooled students, “working at your own pace” would be something that’s unlikely even if in principle possible, but I would certainly expect that a student doing mathematics as advanced as she is would have already finished early: Even if she’s not as good at English and history and so on as she is at mathematics, I’d expect that she’d still be easily good enough at them to pass a state test on them.